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IEEE Transactions on Applied Superconductivity

Macroscopic quantum effects in Josephson systems

Valentina Corato, E. Esposito, C. Granata, A. Monaco, B. Ruggiero, M. Russo, Leo Stodolsky, P. Silvestrini

Published Mar 1, 2001• 7 citations
Publisher

Abstract

Macroscopic quantum effects in Josephson systems have attracted great interest in the scientific community both for the physics involved and in view of applications. We present data on macroscopic quantum tunneling on Josephson junctions. Actually the most fascinating topic is the observation of macroscopic quantum coherence in rf-SQUID. This effect also has implications for quantum computing, because a quantum two-state system represents a single quantum bit, which is the elementary unit of a quantum computer. In this context, here we present a new method to measure quantum coherence between different fluxoid states of an rf-SQUID by using the procedure of "adiabatic inversion". This method offers the possibility of measuring tunneling and decoherence times in the system.

DOI
10.1109/77.919516

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Macroscopic quantum effects in Josephson systems have attracted great interest in the scientific community both for the physics involved and in view of applications. We present data on macroscopic quantum tunneling on Josephson junctions. Actually the most fascinating topic is the observation of macroscopic quantum coherence in rf-SQUID. This effect also has implications for quantum computing, because a quantum two-state system represents a single quantum bit, which is the elementary unit of a quantum computer. In this context, here we present a new method to measure quantum coherence between different fluxoid states of an rf-SQUID by using the procedure of "adiabatic inversion". This method offers the possibility of measuring tunneling and decoherence times in the system.
Macroscopic quantum tunneling (MQT) for a single fluxon moving along a long Josephson junction is studied theoretically. To introduce a fluxon-pinning force, we consider inhomogeneities made by modifying thickness of an insulating layer locally. Two different situations are studied: one is the quantum tunneling from a metastable state caused by a single inhomogeneity, and the other is the quantum tunneling in a two-state system made by two inhomogeneities. In the quantum tunneling from a metastable state, the decay rate is estimated within the WKB approximation. Dissipation effects on a fluxon dynamics are taken into account by the Caldeira-Leggett theory. We propose a device to observe quantum tunneling of a fluxon experimentally. Required experimental resolutions to observe MQT of a fluxon seem attainable within the presently available micro-fabrication technique. For the two-state system, we study quantum resonance between two stable states, i.e., macroscopic quantum coherence (MQC). From the estimate for dissipation coefficients due to quasiparticle tunneling, the observation of MQC appears to be possible within the Caldeira-Leggett theory.
We report experiments on energy level quantization in Nb/AlOx/Nb Josephson junctions while measurements on SQUIDs are in progress. Data on the presence of energy level quantization are shown at temperatures above the classical-quantum regime crossover temperature. This has been possible by extending the measurements of the rate of the escape from the zero-voltage state at higher sweep bias rate in order to induce non-stationary conditions in the energy potential describing the junction dynamics. Data are compatible with extremely low "effective" dissipation in our system. Theoretical predictions on quantum effects related to the presence of non-stationary conditions in the potential associated to a rf SQUID are reported in view of new possible experiments.
We present the design of an on-chip time domain experiment to demonstrate macroscopic quantum coherence in an rf-SQUID, a superconducting loop interrupted by a Josephson junction. If suc- cessful the SQUID will serve as a for a superconducting quantum computer. The chip is currently in fabrication. odinger' s parable, a clear demonstration of rf-SQUID MQC would dramatically challenge our concepts of the quantum / classical boundary. The rf-SQUID MQC state was proposed as a candidate to serve as the for a possible superconducting quantum computer (2). Very recently, spectroscopic experiments showed the energy level structure expected for MQC phenomena in an rf-SQUID (3) and in the very similar persistent current qubit (4). It is our intention to conduct a time domain experiment in which the macroscopic quantum coherent oscillations will be observed directly as they evolve. The Hamiltonian of the rf-SQUID system, under the assumption of no dissipation, is
Recently there has been interest in macroscopic systems which can be described in terms of the quantum dynamics of the same collective variables which describe their classical behavior. In particular, there has been considerable interest in the following questions: (1) Is it possible to observe unambiguous evidence of the quantum-mechanical nature of a macroscopic collective coordinate? (2) In what way is the quantum mechanics of a macroscopic variable different from that of a microscopic variable or, in other words, what is the effect of dissipation on the dynamics of a quantum-mechanical system? Spectroscopic evidence of the quantization of energy levels can be found by measuring the system's response to an applied ac perturbation, exploiting the quantum-mechanical relation between energy and frequency. The specific system studied is a superconducting quantum interference device (SQUID). It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between different fluxoid states. The role of dissipation is discussed in detail, and it is shown that in the case that dissipation is characterized by linear damping in the classical limit, the photon-absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance h/e2{e}^{2}e2. .AE